1. **Problem Statement:** We have a rectangular truss ABCD with points A, B, C, D, E, and F. The truss has segments of lengths 3 m, 4 m, and 3 m horizontally and vertically. A downward force of 60 kN acts at point F. Supports are at A (fixed) and D (roller). We need to analyze the forces in the truss using the method of joints or method of sections. 2. **Key Concepts:** - The method of joints involves isolating each joint and applying equilibrium equations. - The method of sections involves cutting through the truss and applying equilibrium to the section. - Equilibrium equations used are: $$\sum F_x = 0$$ $$\sum F_y = 0$$ $$\sum M = 0$$ - The truss members are assumed to be pin-jointed and only carry axial forces (tension or compression). 3. **Step 1: Calculate support reactions** - Sum moments about A to find vertical reaction at D: $$\sum M_A = 0 = R_D \times 10m - 60kN \times 7m$$ $$R_D = \frac{60 \times 7}{10} = 42 \text{ kN}$$ - Sum vertical forces: $$R_A + R_D = 60 \Rightarrow R_A = 60 - 42 = 18 \text{ kN}$$ - Horizontal reactions are zero since no horizontal external loads. 4. **Step 2: Analyze joint A** - At joint A, vertical reaction is 18 kN upward. - Members AB and AD meet at A. - Use equilibrium equations to find forces in AB and AD. 5. **Step 3: Analyze joint F (where load is applied)** - At F, vertical load is 60 kN downward. - Members BF and EF meet at F. - Use equilibrium to find forces in BF and EF. 6. **Step 4: Use geometry to find member lengths and angles** - For diagonal members like BF and ED, use Pythagoras: $$\text{Length BF} = \sqrt{(4)^2 + (3)^2} = 5 \text{ m}$$ - Angles can be found using trigonometry: $$\theta = \arctan(3/4)$$ 7. **Step 5: Solve system of equations** - Apply $$\sum F_x = 0$$ and $$\sum F_y = 0$$ at each joint to find member forces. - Identify tension (pulling) or compression (pushing) based on sign. **Final answer:** - Support reactions: $$R_A = 18 \text{ kN (up)}, R_D = 42 \text{ kN (up)}$$ - Member forces can be calculated similarly by solving the equilibrium equations at each joint. This approach allows you to find all internal forces in the truss members using the method of joints.